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Solving the Problem of Induction Using a Values-Based EpistemologyAuthor(s): Brian EllisReviewed work(s):Source: The British Journal for the Philosophy of Science, Vol. 39, No. 2 (Jun., 1988), pp.141-160Published by: Oxford University Press on behalf of The British Society for the Philosophy of ScienceStable URL: http://www.jstor.org/stable/687263 .Accessed: 14/10/2012 22:10

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Brit. J. Phil. Sci. 39 (1988), 141-160 Printed in Great Britain

Solving the Problem of Induction Using a Values-Based Epistemology

BRIAN ELLIS

1 Introduction 2 The Empiricist Model 3 Improving the Empiricist Model 4 Induction and Epistemic Conservatism 5 Corroboration 6 Uniformity of Nature 7 Connectivity 8 Solving the Problem

I INTRODUCTION

The problem of induction is to show that our scientific inductive practices are more or less rational. To do this, I shall argue, we need a theory of rationality in which rationality is defined in terms of optimal strategies for maximising epistemic value. The principal aim of this paper is to sketch such a theory, and to explain how it can be used both to justify our inductive practices, in so far as they are rational, and to explain them.

The new theory is one which makes certain epistemic values fundamental, and construes inductive rules as being just more or less useful strategies for promoting these values. It is thus a values-based epistemology. The theories sought by empiricists have usually been rules-based. For their aim has been to show that some particular inductive rule, e.g. the straight rule, is intrinsically rational, and hence that its use is rationally justified. However, for reasons given in Ellis [1965], it is not enough to show that some abstractly considered rule has intrinsically desirable properties. As Goodman has shown, what has to be justified is the way we actually use the rule. And this cannot be done without appeal to our epistemic values.'

1 In Ellis [1965], I argued, much as Nelson Goodman did in Goodman [1954], for the importance of theoretical conservatism as an epistemic value, and claimed that our inductive rules must be applied in theoretically conservative ways if their use is to be rational. More recently, John Clendinnen [1982] and Wesley Salmon [1982] have argued that simplicity and non- arbitrariness are the main considerations in determining whether an inductive rule, such as the straight rule, has been rationally applied-thus giving these epistemic values a central role in their theory.

142 Brian Ellis

The hope of many philosophers is that the problem of induction can be solved by developing a naturalistic theory of rational competence adequate to explain and justify some of our inductive reasoning. I share this hope; but I think such a theory will have to be a values-based theory within which rules have only the status of epistemic strategies, or rules of thumb-much as rules do in act-utilitarianism. First, the inductive rules we use appear to have precisely this character. For there are no inductive rules which can be used indiscriminately, or where the subject matter is theoretically isolated. (See Ellis [1965]). Secondly, it has now been well established empirically that the inductive principles we find most intuitive are often not rational, and that the inductive practices we think are most rational are often not intuitive.2 There is some reason to doubt whether the experimental findings warrant all of the conclusions that have been drawn about the shortcomings of intuitive reasoning (see Cohen [1986]). Even so, the prospects for developing an adequate epistemology which appeals to intuitively valid principles of inductive reasoning do not appear to be good.

Ultimately, the justification of our scientific inductive practices must depend somehow on our intuitive judgements of rationality, as Jonathan Cohen has successfully argued.3 But the appeals to intuition we make when we evaluate inductive rules or strategies are generally to the rationality or otherwise of particular inferences, and so, presumably, to the perceived, epistemically valued, properties of these inferences. The appeal is not to any more intuitively evident principles which may serve as a basis for criticism. Therefore, if our theory is to reflect our practice, what we need is a values-based epistemology rather than a rules-based one. Compatibly with the particularism of our practice of epistemic evaluation, I suppose one could have a kind of Rossian epistemology (cf. Ross [1939]), in which inductive rules had the status of being prima facie rational. But I wish to put greater emphasis on the role of epistemic values in epistemology than Ross did on moral values in ethics.4

The nearest ethical parallel to my position in epistemology is ideal act- utilitarianism. In act-utilitarianism, the right act is that which maximises moral value in the long run. Somewhat analogously, I take the true belief to be that which would maximise epistemic value, if the matter were inquired into with perfect thoroughness by an ideally rational being (assuming no restriction of access to the kinds of information we are in principle capable of obtaining by observation or experiment). Given that the rightness of an act depends on its long-term consequences, judgements of right and wrong are normally defeasible. Consequently, we must distinguish between what it is

2 For a summary of the major findings on the shortcomings of intuitive reasoning, and an excellent discussion of them, see Nisbett and Ross [1980]. See Cohen [1981] and [1986].

4 Good discussions of the varieties of intuitionism in meta-epistemology are to be found in Alston [1978] and especially Dancy [1982].

Solving the Problem of Induction 143

morally right to do and what we are morally justified in doing. Something similar is the case with judgements of truth and falsity, because perfect thoroughness and ideal rationality are idealisations of the kinds of thorough- ness and reasoning of which we are actually capable. Therefore, it is necessary to distinguish between truth and epistemic justification. The truth is what it is epistemically right to believe, not what we may be epistemically justified in believing.

This theory of truth is a pragmatic one. But it differs from other theories in this tradition by the nature of the epistemology on which it is founded. For there are no inductive rules in this epistemology which have more than the status of epistemic strategies. The truth, I want to say, is what it is right to believe in relationship to a specific system of epistemic values, and our rules of inference are just more or less good strategies for constructing the kinds of beliefs and belief systems we value most epistemically.5

The viability of this theory of truth clearly depends on the development of an adequate theory of rationality to define the concept of an ideally rational being. Therefore, the kind of theory we need is a model theory of the sort that is very common in science. This theory must set out to define an ideally rational being, and then, having done so, to explain how people actually think by contrast with how they would think if they were ideally rational.

The requirements on the model are:

1. The ideal of rationality contained in the model should appeal to the normal intellect as a rational ideal. 2. We should be able to use the model successfully to explain our inductive practices, i.e. our inductive practices should be more or less rational, as this is defined in the model; and in so far as they are not, we should be able to explain why. 3. The model should be biologically realistic, i.e. it should be explicable biologically why we should have the basic epistemic values we do.

A theory of rationality which had all of these features would provide an adequate solution to the problem of induction. For it would explain both why we think inductively as we do, and how and why rationally we ought to think inductively. I assume that, biologically, we are value-driven decision systems, and accordingly that the mechanism which shapes our belief systems is value- driven6. That is, I suppose that we have certain inbuilt values which together determine our belief preferences. Among these, I assume that there are certain rational, or epistemic, values which are distinguishable, although perhaps not sharply, from our personal and social values. Our epistemic values determine

5 This theory of truth, which I have elsewhere called an 'evaluative theory' (Ellis [1980]), distinguishes my position from Isaac Levi's. For in his development of a values-based epistemology, Levi supposes truth itself to be an epistemic value. (See Levi [1967] and [1980]). This is something I specifically deny. (See Section 3 below).

6 The case for this has been argued by George Pugh. (See Pugh [1978].)

144 Brian Ellis

what we ought rationally to believe, as opposed to what is otherwise in our interests, or in the interests of society, or is pleasing or comforting to believe.

It is important to distinguish our epistemic values from the biological ends they serve. To flourish, people need reliable, economical, accurate and efficient belief systems which are well adapted to their environments, and applicable to most new situations which may arise. They also need to share many of the beliefs and attitudes of their tribe. Presumably, our epistemic values have been selected to make it possible for us to construct and maintain such belief systems. However, these biological needs are not our epistemic values, and it is not possible to justify our inductive practices with reference to them without circularity. For such ends refer beyond ourselves to our environments, and hence we must have knowledge of our environments if we are to use them for this purpose. Moreover, they may change or disappear as our circumstances change, but our epistemic values are not so externally dependent.

Our most basic epistemic values must be internally assessable things like consistency in our belief systems, beliefs that are empirically certified, well- corroborated beliefs, established beliefs and concepts, beliefs about what is universally the case, and theories establishing certain kinds of links between beliefs or systems of beliefs. Our biological needs have no doubt determined our epistemic values, but we must pursue them for their own sakes, without regard to this fact. It will be argued here that the values just listed are among those which motivate and explain our inductive practices. They are not all equally fundamental, and the list is certainly not complete. But they are all, I think, more or less basic human values which are independent of our social and personal values.

In pursuing knowledge and understanding, we seek to maximise the satisfaction of our epistemic values. And, to the extent that our inductive practices are effective means to this end, I claim that they are rational. For rationality is just the pursuit of epistemic value by appropriate means. Of course, many philosophers will want to define knowledge as knowledge of the truth, and to define truth in some way independently of our epistemic values. To such philosophers, I can offer no prospect of a solution to the problem of induction, because their position is essentially sceptical. But to those who think, as I do, that the truth is what it is right epistemically to believe, a naturalistic solution to the problem of induction may be possible. For the attempt to improve our knowledge and understanding in accordance with our epistemic values, and the quest for truth, are one and the same thing.

2 THE EMPIRICIST MODEL

Empiricists, like most other philosophers, consider empirical certification and consistency to be basic criteria for rationally evaluating beliefs and belief

7 How consistency may be defined epistemologically is explained in Ellis [1979].

Solving the Problem of Induction I45

systems. I call these our empiricist values. According to many empiricists, these values are derivative. They are not innate, as I should say, but derive from the supposedly primary values of truth and avoidance of error.7 Thus, consistency is to be valued, not for its own sake, but because it is a necessary condition for truth. Empirically certified (i.e. perceptually and introspectively acquired) beliefs are generally to be given epistemic priority, not because we have an inbuilt disposition to do so, as I would suppose, but because they are assumed to be known most directly to be true, and hence least prone to error.

According to many empiricists, truth and avoidance of error are the only genuinely primitive epistemic values. So that, on their view, if anything else has epistemic value, its value is derivative. The values of comprehensiveness, verisimilitude and validity, for example, are all said to be explained in terms of these fundamental values. Thus, a more comprehensive theory is generally to be preferred to a less comprehensive one, if neither has been falsified, not because it unifies and makes comprehensible a wider range of phenomena, but because, potentially at least, it contains more truth. As Popper would say, it says more. Verisimilitude, however it is to be measured, is to be valued, not because the criteria we use to gauge it refer to properties which have any intrinsic worth, but because it is supposed that theories possessing these properties are nearer to the truth. Likewise, valid arguments commend themselves for no reason other than that they are necessarily truth preserving, so that if we start with truths we shall never be led into error-although it is not explained why we should prefer to argue validly when we are dealing with ethical propositions, or subjective probability judgements, which, on many empiricist theories, are neither true nor false.

The problem of induction is one that arises within this empiricist framework. For inductive arguments are, by definition, not necessarily truth preserving, and hence invalid. The problem, then, is to explain why an ideally rational being, whose only primary concerns are with truth and avoidance of error, should accept such arguments. The conclusion reached by Hume, and never subsequently overturned, is that there is no rational justification for doing so. Consequently, it is now widely accepted by empiricists that our general beliefs about the world-those which do more than just summarise their known instances-are not rationally held. We hold them, it is said, not because we are rationally entitled to, but because we are creatures of habit, or have found them useful instruments for prediction, and have nothing better to put in their place, or because we have found them unifying, elegant or aesthetically pleasing-at any rate not for reasons which would, in themselves, justify us in believing them to be true.

Now a good theory always accounts for most of the facts in its domain. It may alter somewhat our perception of the facts, and hence our judgement about what a good theory in the area should do. But if a theory restricts the domain of the facts too much, or leaves unexplained most of what it was

146 Brian Ellis

designed to explain, then this is reason to think that the theory is unsatisfactory. A planetary theory which explained only the motions of the outer planets would not be a good theory. It might be acceptable as a step in the direction of understanding planetary motion, but the research programme it defined, of accounting for what the theory left unexplained, would have to be fruitful for it to remain so.

The empiricist theory of rationality, which purports to explain what we may rationally believe, is not a good theory by this criterion. For it leaves most of what it set out to explain, viz., the rationality of science, to be explained in other ways, although no satisfactory explanations have been forthcoming. It can, perhaps, explain our preference for empirically certified beliefs, and certain general facts about the structure of our belief systems. But it does not explain why, rationally, we should accept what most of us would regard as scientifically established. On the contrary, it implies that most of our scientific beliefs are not rationally held, and if nevertheless we hold them, then an empiricist is committed to explaining this fact as due to the influence of non- rational forces, e.g. force of habit, aesthetic preference, or perceived instrumen- tal value. The failure of empiricists to solve the problem of induction is, therefore, a powerful argument against empiricism.

3 IMPROVING THE EMPIRICIST MODEL

To construct a more adequate theory of rationality, we must replace the empiricist model by a better one. To do this, we must try to retain those features of the empiricist model which have explanatory power, or replace them by others capable of doing the same job. Specifically, the values of consistency and empirical certification must be retained, whether or not they are regarded as fundamental.

I think the first step towards improving the model is to reject the assumption that our primary epistemic values are truth and avoidance of error. For we need to break away from the traditional restraints, and there is reason to think that these are not in any case genuine epistemic values. If we reject them, however, we must somehow retain our empiricist values as features of the model, for otherwise we shall just be throwing away the baby with the bath water. My proposal for keeping the baby is that we should regard our empiricist values as primary ones, which are not to be justified in terms of other values, epistemic or otherwise. For, in this way, we can retain those features of the empiricist model which are explanatory without importing the metaphysical concept of truth into the foundations of our theory.

One reason I want to say that truth and avoidance of error are not fundamental epistemic values is that on any theory of truth, other than a subjectivist one, they are not internally assessable, and cannot therefore be the

Solving the Problem of Induction 147

empistemic values which form and shape our belief systems from the start. It might well be biologically necessary for us to have beliefs which are mostly true, and so likely that our epistemic values are adapted to this end. But given any objectivist theory of truth, truth cannot be a fundamental epistemic value.

But I want to go further than this. In my view, truth and avoidance of error are not epistemic values at all. We use various criteria to evaluate beliefs as true or false, but we do not use truth or falsity as criteria for the evaluation of beliefs in any other respect. 'True' and 'false' are terms which function in epistemology like 'right' and 'wrong' do in ethics. They are what I have elsewhere called 'modes of evaluation'. (Ellis [1980]) Now moral rightness is not a moral value, but something which has to be casked in terms of moral values, which are things like justice, happiness, considerateness, honesty, and so on. If we want to understand what moral rightness is, we must understand the value system with respect to which our judgements of right and wrong are made. Likewise, I should say, truth is not an epistemic value, but a mode of evaluation for a system of epistemic values. And if we want to know what truth and falsity are, we must understand the system of epistemic values with respect to which our judgements of truth and falsity are made.

Having made this move, the question then becomes: What are our epistemic values, and how are they interrelated? To retain the virtues of empiricism, I assume that consistency and empirical certification must certainly be two of them, and that both have high priority. Indeed, I should suppose that the value of consistency always overrides. It is clear, however, that we need other values besides these to explain our belief preferences, and hence our judgements of truth, falsity, probability, and so on. For example, the assumption that the world did not exist before people existed is compatible with our empiricist values, as is the assumption that the sun will not rise tomorrow. Hence, if it is irrational to believe such things, as it surely is, it cannot be because it would be contrary to our empiricist values to do so. Therefore, the irrationality of such beliefs must be explained in other ways, or the appearance of irrationality dispelled. I assume that the latter cannot be done. Therefore, to explain the irrationality of such beliefs on the kind of model we are looking for, we must suppose that there are important epistemic values which underlie our judgements of truth and falsity besides the empiricist ones.

I postulate that we are innately disposed to value those kinds of beliefs and systems of beliefs which are biologically useful to us. Perceptually and introspectively acquired beliefs clearly fall into this category. No doubt having a consistent belief system does too. But our survival also depends on our ability to anticipate nature; and this depends largely on our general beliefs and theories. It is to be expected, therefore, that we should attach a good deal of value to our store of such beliefs and theories. We should be reluctant to abandon them, especially those that are well entrenched or have served us well in the past; and if forced to do so, it is to be expected that we should try to salvage what we can from

148 Brian Ellis

them.8 It is also to be expected that we should strive to increase our general knowledge and theoretical understanding, and hence that we should have some epistemic values adapted to these ends.

In the following sections of this paper, I shall describe a number of processes which are evidently involved in the construction, establishment, integration and maintenance of general knowledge-in particular, the processes of generalising, normalising, testing and reconceptualising. I shall not discuss the processes involved in theory construction, or the criteria by which theories are evaluated. My aim is just to describe the basic strategies, and to identify the epistemic values they serve. I shall argue that there are four basic epistemic values which are served by these processes: viz. regularity, epistemic conservatism, corroboration and connectivity. The first provides motivation for the strategies of inductive generalisation and normalisation, and for assuming a kind of 'uniformity of nature' principle. In the area we are concerned with, epistemic conservatism exercises control over what inductive generalisations we may make. It also helps to motivate the normalisation strategy. Corroboration is the value most involved in testing general knowledge, and is therefore fundamental to the process of establishing it and determining its scope. Connectivity is a value concerned with the establish- ment of conceptual connections, and hence with the integration of knowledge. It motivates conceptual changes, and thus serves as a counter to our natural, and proper, epistemic conservatism.

4 INDUCTION AND EPISTEMIC CONSERVATISM

Induction is the primitive strategy we use to arrive at generalisations. Roughly, if something holds in a number of cases without exception, we are naturally disposed to think it will hold generally. What holds in most cases we know about, we are inclined to believe will continue to hold in most cases. What has rarely happened in certain circumstances, we naturally suppose will continue to happen only rarely in such circumstances. I do not think we can be much more precise in our description of the primitive strategy than this, although we are at liberty to theorise that an ideally rational being would generalise according to some more precisely defined inductive rule, such as the straight rule.

The strategy is primitive in the sense that it is unlearned. We could not have discovered it for ourselves, for we should have to have used it to do so. We were not taught it orally, because we needed it to learn at least the vocabulary of the language. For without it we should not know what any term meant, or if we did, that it would continue to mean the same. Nor is there any reason to think that we were ever conditioned to think this way. A crude disposition to " Recent empirical work on theory maintenance supports these general conclusions. See Nisbett

and Ross [1980] Ch. 8 for an excellent review of the psychological literature on this topic.

Solving the Problem of Induction 149

generalise like this seems, therefore, to be a natural tendency. Yet, there are some generalisations we might have arrived at in this way which we should not accept, and others we find quite acceptable. So, however the process of inductive generalisation may be articulated, an important question remains concerning the evaluation of inductive generalisations.

The general principle must be that we tend to value, and therefore seek, generalisations of the kinds that proved useful to us as language and thought evolved. These generalisations will naturally be concerned with the sorts of things we think there are, and therefore, historically, with the sorts of things which were included in our primitive ontologies. Now, we seem naturally disposed to think of our environments as consisting of objects in space and time, possessing various properties, doing various things, and having various effects. Consequently, we are likely to value generalisations concerning any of the sorts of things we think belong to any of these basic ontological categories.

I assume that the ontology we intuitively work with is reflected in the language we use to describe the world. Therefore, since we have names for certain kinds of objects and their properties, and verbs describing certain kinds of actions and events, our primitive ontologies must include kinds of things, actions and events, as well as individuals of these kinds. Therefore, given the general principle that our epistemic preference should be for the sorts of generalisations that have been useful to us in the past, and the presumed utility of our ontologies, we should prefer beliefs about recognised kinds of things to generalisations which are not about recognised kinds, i.e. we should prefer generalisations which derive from conceptually and ontologically conservative descriptions of things. There is nothing sacrosanct about our intuitive conception of reality, as physics has taught us, but it is the natural base from which we must begin; and any change to it needs to be established, and its worth demonstrated, before it can be used as a basis for inductive inferences.

Normally, the logical complements of things, or kinds of things, do not belong to the same ontological categories as the things or kinds they complement-if, indeed, they exist at all. For 'Crows exist' and 'Non-crows exist' are very different kinds of claims. The first is just the claim that things of a certain kind, viz. crows, exist. The second is a much more complicated claim, because, in the sense in which it is true, it implies that there are kinds of things other than crows, and that there are things of at least some of these kinds, i.e. it is doubly existential. Interpreted straightforwardly, in the same way as the claim that crows exist, the claim is simply false. For there is no kind of thing which consists of all kinds of things which are not crows-at least not in my ontology. Likewise, the claim that non-Brian Ellis exists is, if true, just a very odd way of saying that there are individuals other than me. But if it is interpreted as the claim that there is an individual which consists of everything which is not me, then the claim is false. For there is no such individual.

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I do not know how to distinguish between complementary terms which name genuine individuals or kinds from those which do not. I think it is a question of which we think name entities that are required for causal explanations. Certainly, causal involvement is one of our main criteria for what is physically real. But, however the distinction may be made, we all certainly make it, and it is essential to sound inductive reasoning that we should be able to. For inductive arguments must proceed from epistemically preferred descriptions if they are to provide good reasons for their conclusions. And the preferred descriptions are those which, given our current understand- ing of the world, are conceptually and ontologically most conservative. The irrationality of arguing inductively from the existence of white swans or yellow bananas to the conclusion that all non-black things are non-ravens derives, not from the form of the inference, which is sound, but from the irrationality of the conception of such things as non-black non-ravens.9 It is irrational because it violates the requirement of epistemic conservatism.10

The epistemic values of conceptual and ontological conservatism likewise rule out the Goodman inferences. Their irrationality stems from the irrationa- lity of the conceptions from which they proceed. To conceive of emeralds as grue is already to admit into one's ontology a property of grueness, which we could not accept without doing a great deal of violence to our conceptual framework-thus abandoning much of what we think we know for a concept of no proven worth. Our intuition, which, I suggest, derives from the value we attach to established conceptions, is to reject this description along with the inference. Obviously, we cannot reject the description of emeralds as grue on empiricist grounds alone. For the description is compatible with everything that is empirically certified. It does not, however, employ established concepts. Therefore, before we could use such descriptions as bases for inductive inferences, we should need some argument to show that such descriptions were preferable to the established ones. In the absence of such an argument, the requirements of epistemic conservatism rule them out as acceptable bases for inductive inferences.

Epistemic conservatism is not to be equated with dogmatism, or with blind adherence to traditional ways of looking at things. It is neither of these things to refuse to accept the Goodman inferences, or the existence of a white horse as evidence for the generalisation that all ravens are black. Nor is it incompatible

9 I do not deny the relevance of negative-negative cases to the analysis of correlations. Indeed, our natural disposition to ignore such cases is not always rational. (See Nisbett and Ross [1980], Ch. 5). What is irrational is to treat such cases as reflecting correlations between kinds, and so base an inductive argument on them.

10 I should, in fact, be willing to accept a more general thesis of epistemic conservatism than this ontological one-something very close to Sklar's 'methodological' conservatism. For he argues, as I do, that 'Stability of belief is itself a desirable state of affairs and an end to be sought'. (Sklar [1975], p. 389.)

Solving the Problem of Induction 15

with adventurous theorising. If someone can produce a theory with a different ontology from the usual, which is demonstrably superior, by the criteria relevant to theory evaluation, then this theory should be accepted. What it does is establish the onus of proof. Those concepts, laws and theories which have been useful to us are to be retained in the absence of compelling reasons why not.

5 CORROBORATION

The values of epistemic conservatism restrict the range of inductive generalisa- tions which are prima facie acceptable. The value of corroboration contributes to their entrenchment as beliefs and to determining their scope. I think Sir Karl Popper was right to recognise its importance as a value, and that he correctly perceived its role in the development of scientific theory. (See Popper [1959]).

However, Popper was wrong to distinguish, as he did, between corrobo- ration and confirmation, because he left himself without any adequate explanation of the rational preferability of well corroborated beliefs. He cannot say that it is rational to be guided by them because they are most likely to be true. Nor can he say that having been well corroborated they are likely to continue to be. Indeed, on his own theory, we have no reason to believe that falsified theories will not always be corroborated in future, and hence no more reason to trust corroborated theories than uncorroborated ones. In my view, Popper needs corroboration as a basic epistemic value, and a theory of rational belief which recognises this value. The more often, and the more widely varied the circumstances, in which a law, theory or generalisation has been corroborated, the more rational it must be to believe it, and hence the greater its epistemic probability.

The value of corroboration, like that of epistemic conservatism, derives from the proven utility of corroborated beliefs. It is not that we know in advance that corroborated beliefs will continue to be corroborated. What we know is that they have, or would have, been successful predictors. Now the general principle from which our epistemic values may be derived is that the sorts of beliefs which have been useful to us in the course of evolution are the ones we are likely to value epistemically, and therefore to consider belief-worthy. So corroborated beliefs should, by this principle, be considered worthy of belief- the more so, the more often, and the more varied the circumstances, in which they have been corroborated.

The point of varying the circumstances of corroboration is to test a hypothesis more widely. If the hypothesis is that all As are Bs, and if all instances of this generalisation that have been observed are As that are Cs, and if it is plausible, on background information, that an A's being a C is relevant to its being a B, then the corroboration we have obtained may only be for the more restricted hypothesis that all As that are Cs are Bs. So, to remove this

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doubt about the scope of the corroboration, we must examine some As that are not Cs to see whether they too are Bs. Background information is thus obviously relevant to corroboration. For we need to know what sorts of factors might limit the scope of a generalisation to know what tests to perform. Blindly repeating tests under more or less similar circumstances is not a good way to corroborate a hypothesis. For it leaves open the possibility that the generalisa- tion holds only in these circumstances.

On the other hand, if we thought that observation itself, or time or place of observation, might be a factor limiting the scope of any generalisation, then strong corroboration of unrestricted generalisations would be impossible. For while observing As that are Bs may make it reasonable to believe that all As that have been or will be observed are Bs, or that all As in our spatio-temporal region are Bs, we should not be able to corroborate strongly the more general hypothesis that all As are Bs. I assume, however, that strong corroboration of hypotheses of unrestricted scope or generality is possible, for otherwise the laws and theories of science could not be well corroborated. Therefore, we must be strongly disposed to believe, independently of corroboration, that what holds for us in our own spatio-temporal region holds generally. That is, we must operate with a sort of 'uniformity of nature' principle. Why this should be so will be considered presently.

It is impossible to say, without reference to our background theories, how strongly a hypothesis is supported by corroborative evidence. It depends how unequivocal the evidence is, how plausible the hypothesis is given our background understanding, how probable we should take the evidence to be independently of the hypothesis, how broad the scope of the hypothesis being tested, and whether there are reasons for thinking that some scope restrictions on the hypothesis being tested may be necessary.

If the degree of corroboration provided by the evidence e for the hypothesis h is measured by P(h/e) - P(h), normalised to a zero to one scale,11 then

1. S(h/e)= P(h/e) x P(.- e/.-

h)

That is, the more probable the hypothesis, given the evidence, and the more improbable the evidence, given the denial of the hypothesis, the greater the degree of corroboration. Thus, the strongest corroborations of our hypotheses are to be obtained from their least probable consequences.

Also, if h entails g, and g entails e, then the following chain rule holds:12

2. S(h/e) = S(h/g) x S(g/e)

11 I have argued in detail for this as a measure of degree of positive support in Ellis [1970]. The normalising factor required is 1/(1 - P(h)).

12 This striking result is a convincing demonstration of the importance of test variety; and reflects favourably on the normalised scale of evidential support, since the chain rule does not hold for other measures of support.

Solving the Problem of Induction 153

Consequently, if the evidence we have all corroborates g, and g has been sufficiently corroborated, there is no point in seeking further evidence of this kind. To increase support for h, we must seek evidence of a different kind, viz. evidence for some consequence of h which is not a consequence of g. If h is the hypothesis that all swans are white, it is not to the point to go on examining European swans, once the hypothesis g that all European swans are white has been sufficiently corroborated. For the maximum degree of corroboration for h obtainable this way is S(h/g), which, given our background knowledge of bird colour variation with geographical location, may be quite low.

These two results define and explain the importance of test severity and test variety in the process of corroboration. If a hypothesis survives sufficiently many and various tests of enough severity, it will be well-corroborated. And a well corroborated hypothesis, I hold, is one which, other things being equal, we ought rationally to believe. Hence, there may come a point, in the process of corroboration, when the evidence for a hypothesis becomes compelling, and if it is contrary to anything else we believe, it may be necessary to revise this belief. The claims of epistemic conservatism may thus be overcome by the corroboration of hypotheses.

6 UNIFORMITY OF NATURE

It is often held that induction depends on the assumption that nature is uniform, i.e. that all things are governed by strictly universal laws. However, no principle of the uniformity of nature can be formulated which will justify our inductive practices. For it cannot be used to validate any inductive inferences, unless we can identify those local regularities which instantiate universal laws. Moreover, the assumption itself needs justification, since it is not a priori, nor even generally accepted. The Ancient Greeks, for example, expected to find perfect regularity only in the heavens, and in the abstract world of the Forms. And many people today would exempt human actions from the ambit of universal laws. So the assumption is not justified either way. But even if it were, we do not appear to need it. The Ancient Greeks argued inductively, though they did not make this assumption.

Nevertheless, there is something to the suggestion that belief in the uniformity of nature supports our inductive practices. For we seem naturally to be disposed to search for regularities or uniformities in nature, and to see any deviations from the regularities we think we have discovered as being superimposed by extraneous forces. It is not that nature, as we find it, is uniform, even within the range of our observations. But we are inclined to assume it is, nevertheless, and to conceive of things as instantiations of general regularities, distorted though they may be by their peculiar circumstances or histories. We seem thus to be natural regularity seekers. We are not content with local generalisations. Whatever holds locally, we are naturally inclined to

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suppose holds generally, unless there are special reasons (such as those the Greeks had, or libertarians have) to think otherwise. Newton summed up the attitude in the third of his 'Rules of Reasoning in Philosophy':

The qualities of bodies which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever. (Thayer ed. [1953], p. 3)

To explain this attitude, which presupposes the uniformity of nature, I assume that the drive to discover regularity is primitive. It is not that our inductive reasoning is justified by our belief in the uniformity of nature. It is rather that the epistemic values which determine the patterns of our inductive reasoning naturally incline us toward this belief. Belief in the uniformity of nature cannot justify our inductive inferences; nor can that belief be justified inductively. But there is an underlying attitude, which does much to explain both, viz. the primitive desire to discover regularity in nature.

The value of regularity manifests itself in a number of ways. Most obviously, it inclines us to believe that generalisations which are found to hold locally also hold generally. But more importantly, it drives us to search for deep or

underlying regularities in phenomena, where no such regularities are appar- ent, or if apparent, then not unblemished.

The search for regularity has led to the development of a number of

strategies. Of particular importance are the strategies of normalisation and idealisation. The first of these is a primitive strategy for concept formation; the second, a basic strategy for theory construction. The normalising strategy is

primitive, at least in the sense that it is pre-verbal. For without it we could not

acquire knowledge of the concepts or grammar of a language. The strategy of idealisation is probably not primitive in this sense. It appears to be an extension of the strategy of normalisation--one which is useful when the conditions for the applicability of the normalising strategy are not satisfied.

To normalise is to distinguish between normal and abnormal cases in order to formulate or defend some generalisation, and to isolate any real or apparent counterexamples. A normalised generalisation is then seen as being the statement of some underlying regularity; and the counterexamples are seen as

being as more or less superficial distortions produced by special conditions or circumstances.

Philosophers have not paid much attention to the strategy of normalisation which is standardly used in connection with empirical generalisations. Yet the

normal/abnormal distinction, and its many variants, is as fundamental and

pervasive as any in our language. We apply it to people, stars, modes of behaviour, speech patterns, chemical reactions, circumstances, samples, and

just about everything else. Indeed, to conceive of things in terms of norms and exceptions is normal practice, and it seems to come quite naturally to us. No

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theory of human rationality can be satisfactory, therefore, if it gives no account of it.

Evidently, the disposition to normalise is primitive. For without a readiness to distinguish between normal and abnormal cases, and thus maintain generalisations in spite of exceptions, we could never learn to speak. Most of our empirical concepts depend for their identity on the set of normalised generalisations we accept concerning them. Thus our concept of man is not defined by the set of strictly universal generalisations we accept about men. There are too few such generalisations, and they are not specific enough to

distinguish men from many other animals. What distinguishes men at the perceptual level, which is the level at which our concept is acquired, is what they normally look like, what capacities they normally have, what features are normally present, and so on. And the identity of our initial concept of a man must depend on these. The same is true of most of the other empirical concepts we need to acquire a knowledge of language. Therefore, the normalising strategy must be primitive enough for us to be able to operate with it at this level.

7 CONNECTIVITY

The desire to understand things is the main motivation for scientific enquiry, and we should expect there to be several primary epistemic values concerned with this activity. Here I shall focus on one which I think is important. I call it the value of connectivity, because it is concerned with the establishment of conceptual connections, and hence with the theoretical integration of knowledge.

The inductive practices I have considered so far have been more or less straightforward inferences from samples to populations. Those involved in the establishment of conceptual connections are much less straightforward. Indeed, they include the full range of strategies described by Imre Lakatos in his 'Proofs and Refutations' (Lakatos [1963]).

The strategies of normalisation and idealisation enable us to identify certain underlying regularities in nature, and to define the irregularities which remain to be accounted for. The acceptability of the norms and ideals we thus arrive at depends on how well we can explain what is not normal or not ideal relative to these concepts and principles. Hence our normalising and idealising strategies cannot in themselves satisfy our desire to discover uniformity or regularity in nature; they merely set an agenda for doing so.

To explain why some As are Bs, given that As are not normally or ideally Bs, we must try to discover some characteristics of the As, or the circumstances in which we find them, which are sufficient to account for their B-ness. So, minimally, we must look for generalisations of the form, 'All As that are Cs are Bs'. However, not every acceptable generalisation of this form is explanatory.

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For example, 'All As that are Bs are Bs' is not. To be explanatory, the condition C cannot be more than contingently sufficient for the B-ness of As.

There may, however, be several contingently sufficient conditions for the B- ness of As. Thus, all As that are Ds may be Bs, as well as all As that are Cs. Moreover, there may be As that are Bs which are neither Cs nor Ds. So we may have to say that some As are Bs for other reasons. Furthermore, the explanatory hypotheses we arrive at may themselves turn out to have exceptions, and so have to be normalised. For example, we may find that C is only normally a sufficient condition for an A being a B. And then, no doubt we should want to know what sometimes prevents C from having its normal effect. The search for explanations of the exceptions to our normality generalisations, or to the framework principles postulated as governing the behaviour of the idealised theoretical entities of science, may thus lead to many complications.

Proliferating subsidiary explanations in this kind of way is intrinsically unsatisfying, and if it seems that there are too many reasons why an A may be a B, then we are likely to think that we have not got to the heart of the matter. For example, we may think that the appearance of diversity amongst the reasons for B-ness is superficial, or that the allegedly similar effects are fundamentally dissimilar. In extreme cases, we may think that the problem is generated by the norms or ideals we have adopted, and so seek some other way of conceptualising the subject matter of our enquiry.

Our search thus appears to be for conditions which are not only sufficient for the effects we wish to explain, but also, if possible, necessary. And persistent failure to discover conditions which are both necessary and sufficient for a given effect can be a powerful incentive to reevaluate the conceptual framework within which the problem arises.

The discovery of such conditions for things is evidently intellectually satisfying. So, presumably, some epistemic value attaches to the knowledge of them. This is the value I call 'connectivity'. The source of this value, I suppose, is that such knowledge forges the conceptual links we need to build up an adequate conceptual framework for interpreting reality, i.e. it is an important contribution to our understanding of things. If we know that A is a necessary and sufficient condition for B, then the knowledge that something is a B is not isolated, but linked to the knowledge that it is an A. Hence, if we can discover what makes something an A, we may also find out what makes it a B. Or perhaps we shall find that there is some common cause for both A-ness and B- ness. Either way, the knowledge that something is a B may be located in a systematic framework, and so better understood.

The biological advantage of establishing such connections between items of knowledge is the increased efficiency and precision of the knowledge system it generates. If we know that As are normally Bs, then that may sometimes be good enough. But if we know that all and only As that are Cs are Bs, then the

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knowledge is more precise, and we have at least the beginnings of a theory of B- ness. Moreover, if we know this, then the fields of evidence for C-ness and B- ness are both increased. For now, any evidence that an A is a B is immediately evidence that it is a C, and conversely. Consequently, the establishing of such a conceptual tie between C-ness and B-ness expands the range of inferences we can draw from the evidence we have, and consequently increases the efficiency of our knowledge system.

I postulate that the desire to know what makes something the case, in the sense of knowing necessary and sufficient conditions for it, is primitive. The interest we have in knowing this is not just the interest of controlling or anticipating nature, although this may help to explain why we have it. For the desire to know the necessary and sufficient conditions for things is manifest even where there is no possibility of control, or the events we are seeking to explain are unlikely to recur. The interest is rather in satisfying our intellectual curiosity, our desire to understand what makes things so.

This desire is partly satisfied by the discovery of conditions which are either necessary or sufficient, for such discoveries also increase the range of inferences we are able to draw. But conditions which are both necessary and sufficient appear to be especially significant to us, and we are often willing to sacrifice content, and to modify or refine our concepts to establish such connections, as Lakatos' history of Euler's theorem amply demonstrates. (ibid.) If all As are Bs, but some Bs are not As, then A-ness does not adequately account for B-ness. On the other hand, A-ness cannot by itself account for B- ness if there are any As that are not Bs. Therefore, we can have an adequate theory of B-ness if we can find some condition which is both necessary and sufficient for B-ness.

The desire to discover necessary and sufficient conditions for things is thus a very important ingredient of our desire to understand things. So it is not surprising that we should sometimes be willing to modify our concepts, or to reduce the empirical content of our assertions, in order to create such connections. Consider the Lakatosian history of Euler's theorem. (ibid.) As the classroom discussion opens, the concepts of polyhedron, polygon, face, edge and vertex are all somewhat amorphous normality concepts. By the end, all of these concepts have been shifted or focussed, various conceptual links have been established (provisionally, at least) between them, and Euler's theorem has been embedded in a comprehensive theoretical network.

From a Popperian point of view, the changes which have occurred are content-reducing. For the tighter the conceptual links become in the process of articulating the theory, the more the propositions asserted take on the character of conceptual truths, and the less falsifiable they become. Counter- examples become not only more difficult to find, but more difficult to conceive. We are of course better able to predict the properties of polyhedra, given the theory, than we were before, because we had to learn how to apply the theory

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in the process of refining and developing it. The theory was improved, however, more as an instrument for conceiving and analysing polyhedra, and so predicting their properties, than as a set of independently testable assertions concerning them. And the scientist, like the carpenter who acquires a better set of tools, finds it more difficult to blame his or her equipment if things go wrong.

The value of connectivity is a basic value in theory development. For the establishment of new conceptual ties inevitably increases our understanding of things. I do not say that this is all that is involved in improving our understanding, but forging new conceptual links is at least an important part of it. The value is one which, more than any other, leads to conceptual innovations, and is therefore a counter to our natural (and proper) epistemic conservatism. It is also a value which is often opposed in its effects to the aim of making our theories more testable. The more tightly our knowledge system is integrated the less vulnerable to empirical refutation many of its elements will become.

8 SOLVING THE PROBLEM

To solve the problem of induction, it will be necessary to develop in detail the kind of epistemology I have sketched here, and show that it is adequate to explain, and, in so far as they are rational, justify our scientific inductive practices. I do not claim to have made more than a start on this. The list of epistemic values I have given is certainly incomplete, and the values contained in it are probably not all equally fundamental. For example, there is reason to think that there is a value of simplicity, related to economy of thought, which is at least as fundamental as any that I have so far mentioned. There is also, as I have argued elsewhere (Ellis [1980]), a value of objectivity, which is related to the social functions of knowledge. On the other hand, I should not be surprised if some of the values I have listed could be shown to be dependent on others. Henry Krips, for example, has argued that epistemic conservatism is not an independent virtue. (See Krips [1982].) I am convinced, however, that this is the right approach. To solve the problem of induction we need to define a biologically plausible ideal of rationality on which our inductive practices can be explained. I have assumed that, biologically, we are value-driven decision systems. If this is right, then what we must have is a values-based epistemology. The aim of this paper has been to outline such a theory.

An ideally rational being, I hold, is one that is at least: consistent; has a natural tendency to generalise widely, but is epistemically conservative in the generalisations it makes; seeks corroboration for its beliefs, and, other things being equal, believes more strongly in those that are better corroborated; is driven to seek underlying regularity in nature, and so conceive of things in terms of norms and exceptions, or, by extension, in terms of ideal and actual

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states of affairs, and finally; strives to increase its understanding by seeking to establish conceptual connections. An ideally rational being must also be supposed to have a belief system which is perfectly integrated according to its own standards of rationality.

But how might all this solve the problem of induction? Let us suppose that we have at last developed a values-based epistemology which is adequate to explain our scientific inductive practices, i.e. a theory on which our inductive practices either turn out to be rational according to the theory, or not rational, but for reasons we are persuaded are correct. Our inductive practices are now, by hypothesis, embedded in an adequate theory of human rationality. Hence we can now say what makes them rational. They are rational to the extent that they are the practices of an ideally rational being. But then, you may ask, why should we be rational in this sense? Why should we accept the value system of such a being? To this my answer is 'Because you are human'. For these are your epistemic values, and you cannot, like a god, step outside your value system to judge whether or not it is rational to have them.

La Trobe University, Melbourne, Australia

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